Question

The teachers are setting up a socially distanced summer retreat to discuss the 2021-

2022 school year. In order to rent the facilities there is a $1295 cost and then each
person will need to pay for own site for camping which is $45 for the weekend.
Mr. Jones would agree to organize the trip if he would have his costs paid for. How
many people would need to attend in order for the cost to be less than $60 per person? Please include a table, graph, and rule.

NO LINKS or anything like that, help ASAP.

Answer 1

9514 1404 393

Answer:

91, including Mr. Jones

Explanation:

The total cost for n people to go on the trip will be ...

C(n) = 45n +1295

If Mr. Jones does not pay anything, this cost is divided among the remaining (n-1) persons, so the cost per person is ...

`c(n)=(C(n))/(n-1)\\\\c(n)=(45(n-1)+45+1295)/(n-1)=45+(1340)/(n-1)`

We want to find n such that c(n) < 60.

`45+(1340)/(n-1)<60\\\\(1340)/(n-1)<15\qquad\text{subtract 45}\\\\(1340)/(15)<n-1\qquad\text{multiply by $(n-1)/(15)$}\\\\90(1)/(3)<n\qquad\text{add 1}`

A total of 91 people would need to attend in order for the cost per person to be less than $60.